Electromagnetic Waves

Linear and Circular Polarization of EM Waves
The plane wave (6) and (11) is a wave with its electric field vector always
in the direction ɛ1. Such a wave is said to be linearly polarized with
polarization vector ɛ1. The wave described by (12) is linearly polarized
with polarization vector ɛ2 and is linearly independent of the first.
The two waves :
E1 = ɛ1E1e i k·x−iωt , E2 = ɛ2E2e i k·x−iωt
with (17)
Bi = √ µɛ k × Ei
, i = 1, 2
k
Can be combined to give the most general homogeneous plane waves
propagating in the direction k = kn,
E(x, t) = (ɛ1E1 + ɛ2E2) e i k·x−iωt
E(x, t) =
(18)
ɛ1|E1| + ɛ2|E2|e i(φ2−φ1)
e ik·x−iωt+iφ1 (19)
The amplitudes E1 = |E1|e iφ1 and E2 = |E2|e iφ2 are complex numbers in
order to allow the possibility of a phase difference between waves of
different polarization.
Electromagnetic Waves